abeka plane geometry test 3

when 2 st. lines are cut by a trans. and the int. angles on the same side of the trans. contain 110 degrees and 70 degrees, the 2 lines are //

true

if a line is // to 1 of 2 perpendicular lines, it is also // to the other line.

false

if 2 angles are sup. to the same angle, they are sup. to each other.

false

the sum of 2 acute angles is an obtuse angle

false

if AB is the perpendicular bisector of segment CD, then AB passes through the midpoint of CD.

true

if 2 adj. angles are sup. then their 2 isn't. sides are perpendicular.

false

2 triangles are congruent if 3 sides of one triangle are = respectively to three sides of the other triangle.

true

if only 2 angles of a triangle are =, it will logically follow (not necessarily in one step) that the triangle is isos.

true

if 2 adj. angles are complementary, a side of one of the angles is perpendicular to a side of the other angle.

true

if 2 sides of a triangle are unequal, the angle opposite the greater side is the smaller angles.

false

list 5 reasons for proving two triangles are congruent.

SSS, SAS, ASA, LA, LL

list 3 general ways to prove that 2 angles are =, excluding the definition.

CPCTE, vert. angles, alt. int. angles of // lines

what must 2 angles share in common in order to be called adj?

same vertex and same side between them

write the // post.

through a given pt. 1 and only 1 st. line can be drawn // to a given line

what is the supplement of a 47 degree angle?

133 degrees

what is the complement of a 36 degree 27' angle?

53 degrees 33'

the sum of the angles of a triangle is...

180 degrees

a general statement accepted without proof to be true is a(n)...

axiom

the measure of each angle of an equilateral triangle is ___ degrees

60 degrees

when 2 lines intersect they form vertical angles that are...

equal

a statement that is not self-evident but proved by a chain of reasoning is a(n)...

theorem

base angles of an isos. triangle are...

equal

a triangle having no = sides is a ___ triangle

scalene

2 lines that form rt. angles are called...

perpendicular lines

if 2 // lines are cut by a trans. then the sum of the 2 ext. angles on one side of the trans. is...

180 degrees

26

45 degrees

27

60 degrees

28

108 degrees

29

51 degrees

30

109 degrees

proof: statements
1. AC=BD, CB=DA
2. AB=BA
3. T. ABC = T. BAD

reasons

1. given
2. identity
3. SSS

proof: statments
1. AB and CD bisect each other
2. AO=BO, CO=DO

3. A. AOC=A. BOD
4. T. AOC=T. BOD
5. AC=BD, A. CAO=A. DBO
6. AC//BD

reasons

1. given


2. def. of segment bisectors
3. 2 lines intersect to form = vert. angles
4. SAS


5. CPCTE


6. if 2 lines are cut by a trans. to form = alt. int. angles, then the lines are //

proof: statements
1. AB=AC, angle 1 = angle 2
2. angle 1 + angle BAD = st. angle
angle 2 + angle CAD = st. angle
3. angle 1 + angle BAD = angle 2 + angle CAD
4. angle BAD = angle CAD
5. AD = AD
6. T. ABD = T. ACD
7. angle B = angle C

reasons

1. given


2. the sum of all the angles about a pt. on one side a st. line is a st. angle


3. all st. angles are =



4. - ax.



5. identity
6. SAS

7. CPCTE